Title: "Locally definable groups in o-minimal structures." Abstract: What I find fascinating in the study of definable groups is the rich interplay between algebra, topology and logic (= definability). The simplest manifestation of this fact is the following: a definable abelian group is divisible (an algebraic notion) if and only if it is definably connected (a definable-topological notion). The locally definable category is more difficult to understand because we lack the finiteness phenomena typical of the definable category. For instance any countable group (e.g. the rationals) is locally definable. Nevertheless many of the tools developed in the definable category (logic topology, o-minimal algebraic topology, etc.), carry over to the locally definable context. I will explore some these topics focusing (maybe) on (a selection of) the following: 1) finiteness of the n-torsion subgroup in locally definable connected divisible abelian groups (work in progress with M. Edmundo and M. Mamino); 2) homeomorphism type of definable abelian groups (with E. Baro); 3) abstract versus topological group extensions (with Y. Peterzil and A. Pillay).